NIntegrate
NIntegrate(f, {x,a,b})
computes the numerical univariate real integral of
f
with respect tox
froma
tob
.
See:
- Wikipedia - Numerical integration
- Wikipedia - Trapezoidal rule
- Wikipedia - Romberg’s method
- Wikipedia - Riemann sum
- Wikipedia - Truncation error (numerical integration)
- Wikipedia - Gauss-Kronrod quadrature formula)
Examples
>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1})-0.0208333333333333
LegendreGauss is the default method for numerical integration
>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->LegendreGauss)-0.0208333333333333
>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Simpson)-0.0208333320915699
>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Trapezoid)-0.0208333271245165
>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Romberg)-0.0208333333333333
>> NIntegrate(Exp(-x^2),{x,-Infinity,Infinity}, Method->GaussKronrod)1.772453850905516
>> NIntegrate(Cos(200*x),{x,0,1}, Method->GaussKronrod)-0.004366486486070
Other options include MaxIterations
and MaxPoints
>> NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1), {x,0,1}, Method->Trapezoid, MaxIterations->5000)-0.0208333271245165
Related terms
D, DSolve, Integrate, Limit, ND
Implementation status
- ☑ - partially implemented